The Renaissance astronomer and astrologer Johannes Kepler is best
known for his discovery of the three principles of planetary motion,
by which he clarified the spatial organization of the solar system.
Moreover, he founded modern optics by presenting the earliest correct
explanation of how human beings see. He was the first to set forth
accurately what happens to light after it enters a telescope, and he
designed a particular form of that instrument. His ideas provided a
transition from the ancient geometrical description of the heavens to
modern dynamical astronomy, into which he introduced the concept of
physical force.

On December 27, 1571, in the German town of Weil der Stadt, then a
"free city" within the Holy Roman Empire, Johannes was born
prematurely, the offspring of an unhappy marriage. His father was a
ne'er-do-well mercenary soldier, his mother the quarrelsome daughter
of an innkeeper. Small in stature, Johannes never enjoyed robust
health, but his superior intelligence was recognized even when he was
a young child. Coming from a poor family, he would have received no
education had not the dukes of Wrttemberg adopted the enlightened
policy of providing generous scholarships for the bright sons of
their impoverished subjects.

With such help Kepler in 1587 was able to attend the University of
Tbingen, where he had the good fortune to study astronomy under
Michael Mstlin, a professor who may have been unique in his day, for
he was convinced that the astronomical system propounded by Nicolaus
Copernicus was basically true: the Earth is a planet that rotates
daily around its own axis and revolves annually around the Sun.
Kepler's youthful acceptance of Copernican astronomy profoundly
affected the subsequent course of his life.

After obtaining the B.A. in 1588 and the M.A. in 1591, Kepler planned
to become a Lutheran minister. But in 1594, during his last year of
training in theology at Tbingen, the teacher of mathematics in the
Lutheran high school of Graz, in Austria, having died, Kepler was
strongly recommended by the Tbingen faculty to fill the vacancy.
Kepler did not finish the theology course at Tbingen but went to Graz
the same year. On a summer day in 1595, while he was teaching a
class, a spectacular idea flashed through his mind. Ancient Greek
geometry had proved that there were five regular solids, or "Platonic
bodies": tetrahedron (pyramid), cube, octahedron (formed by eight
equilateral triangles), dodecahedron (12 pentagons), and icosahedron
(20 equilateral triangles). The ancients knew that these five solids
could be enclosed in a sphere, and that there can be no additional
regular solids. Sustained by a vision of mathematical harmonies in
the skies, a vision he derived from the philosophy of Plato and the
mathematics of the Pythagoreans, Kepler tried to relate planetary
orbits with geometrical figures.

According to Copernican astronomy there were six planets, whose
orbits were regulated by the turning of invisible spheres. But why
were there only six planets and not nine or 100? Was the cosmos so
constructed that one of the five regular solids intervened between
each pair of the unseen spheres, which carried the six Copernican
planets? This nest of alternating planets and regular solids
constituted the main theme in Kepler's Prodromus Dissertationum
Mathematicarum Continens Mysterium Cosmographicum ("Cosmographic
Mystery"), which he published in 1596 under the auspices of the
Tbingen faculty. The Platonic and Pythagorean components in Kepler's
conception of celestial harmony, however mystical in origin, helped
to lead him to the three principles of planetary motion now known by
his name.

Kepler sent copies of his first major work to a number of scientists,
including Tycho Brahe, who was soon to become the imperial
mathematician of the Holy Roman Empire. Although Brahe did not agree
with the underlying Copernican foundation of Kepler's Mysterium
Cosmographicum, he was so impressed by the author's knowledge of
astronomy and skill in mathematics that in 1600 he invited him to
join his research staff in the observatory at Benatek (now Bentky nad
Jazerou), outside Prague. When Brahe died the next year, Kepler was
promptly appointed his successor as imperial mathematician. His first
publication at Prague, De Fundamentis Astrologiae Certioribus (1601;
"The More Reliable Bases of Astrology"), rejected the superstitious
view that the stars guide the lives of human beings. Nonetheless, his
deep feeling for the harmony of the universe included a belief in the
harmony between the universe and the individual, and his skill in
astrological prediction was much in demand.

While Kepler was watching a rare conjunction of Mars, Jupiter, and
Saturn in October 1604, a supernova appeared that remained visible
for 17 months. This event was evidence that the realm of the fixed
stars, considered since ancient times as pure and changeless, could
indeed experience change. He published the results of his
observations in 1606 as De Stella Nova in Pede Serpentarii ("The New
Star in the Foot of the Serpent Bearer").

Kepler now had access to Brahe's incomparable collection of
astronomical observations, the result of decades of unremitting and
painstaking toil by the greatest naked-eye observer of the heavens
and the leader of a highly qualified team of astronomers. As a member
of the team, Kepler had been assigned to investigate the planet Mars.
But, before he could use the raw observations, Kepler felt that he
had to solve the problem of atmospheric refraction: how is a ray of
light, coming from a distant heavenly body located in the less dense
regions of outer space, deflected when it enters the denser
atmosphere surrounding the Earth?

Kepler incorporated his results in a book that he modestly entitled
Ad Vitellionem Paralipomena, Quibus Astronomiae Pars Optica Traditur,
(1604; "Supplement to Witelo, Expounding the Optical Part of
Astronomy"); Witelo (Latin Vitellio) had written the most important
medieval treatise on optics. But Kepler did much more than add to his
work. He made an analysis of the process of vision that provided the
foundation for all of the advances in the understanding of the
structure and function of the human eye. Kepler wrote that every
point on a luminous body in the field of vision emits rays of light
in all directions, but that only those rays can enter the eye that
impinge on the pupil, which functions as a diaphragm. He stated that
the rays emanating from a single luminous point form a cone, the
circular base of which is in the pupil. All of the rays are then
refracted within the normal eye to meet again at a single point on
the retina, identified by Kepler as the sensitive receptor of the
eye. If the eye is not normal, the second short interior cone comes
to a point not on the retina but in front of it or behind it, causing
blurred vision. For more than three centuries eyeglasses had helped
older persons to see better. But nobody before Kepler was able to
explain how these little pieces of curved glass had worked.

After the invention of the telescope had been reported to Galileo,
who promptly proceeded to make his astounding discoveries, Kepler
applied the same ideas concerning optics to the explanation of how
the telescope works. Although Galileo's findings were received in
general with skepticism and ridicule, Kepler acknowledged the
Italian's accomplishments in his Dissertatio cum Nuncio Sidereo Nuper
ad Mortales Misso a Galilaeo Galilaeo in 1610.

Galileo did not return the compliment. He chose to ignore the
epoch-making results Kepler had published the preceding year. (See
Kepler's theory of the solar system.) In his Astronomia Nova ("New
Astronomy") of 1609, Kepler had demonstrated that the orbit of the
planet Mars is an ellipse. Although it had been believed since
antiquity that the planets, being heavenly bodies, were perfect and
therefore could move only in perfect circles or combinations of
circles, Copernicus had correctly classified the Earth as one of the
planets; and it was fully accepted that the Earth was far removed
from perfection. Kepler extended Copernicus' reasoning to the other
planets and was the first to declare that the other planets resemble
the Earth in being material bodies. That a material body, being
imperfect, need not travel in a perfectly circular orbit was a
conclusion made by Kepler after he tried unsuccessfully to fit the
orbit of Mars to Brahe's observations in every possible combination
of circles his ingenuity could devise. Because none of them worked,
he tried noncircular paths until he found the true solution: Mars
revolves in an elliptical orbit with the Sun occupying one of its two
focuses.

The pre-Keplerian dogma that permitted only circular paths entailed
the concept of uniform motion--i.e., the moving body or point must
traverse equal arcs in equal intervals of time. Such a conception of
uniform motion as measured along an arc was, of course, incompatible
with an elliptical orbit. But Kepler found an alternative form of
uniformity. This new uniformity equated equal areas with equal times.
With the Sun remaining stationary in one focus of the ellipse, the
planet, while revolving along the periphery of its elliptical orbit,
would sweep out, in equal intervals of time, equal areas of the
ellipse, not equal arcs along the periphery of the ellipse.

In 1619, 10 years after Kepler published these first two principles
of planetary motion (the elliptical orbit and equality of areas), he
published the Harmonice Mundi (Harmonics of the World), in which he
expounded his third principle, which related a planet's mean distance
from the Sun to the time it takes to complete its elliptical orbit
around the Sun. The cube of the distance proved to be in a constant
ratio to the square of the time required for all the planets to
complete such an orbit. The enunciation of this rule (which is
sometimes called the 3/2 ratio) completed Kepler's contribution to
the understanding of planetary motion and helped to prepare the way
for Sir Isaac Newton's exposition of universal gravitation, which
affects all of the material bodies in the physical universe.

Meanwhile, Kepler's patron, the Holy Roman Emperor, had been
compelled by his brother to abdicate, and Kepler himself had found it
desirable to leave Prague, then the capital of the empire. Although
he was reappointed imperial mathematician by the new emperor, Kepler
moved to Linz, in Austria. His first wife had died in Prague; Kepler
remarried in 1613. Once, when buying supplies for his new home,
Kepler became unhappy about the rough-and-ready methods used by the
merchants to estimate the liquid contents of a wine barrel. Because
the curved containers they used were of various shapes, Kepler sought
a mathematical method for determining their volumes. Following the
model established by Archimedes, the most talented mathematician of
antiquity, Kepler, in his volumetric researches, investigated the
properties of nearly 100 solids of revolution--made by rotating a
two-dimensional surface on one of its axes--that had not been
considered by Archimedes. Starting with an ordinary wine barrel,
Kepler enormously extended the range of Archimedes' results. He did
so by refusing to confine himself, as Archimedes had done, to cases
in which a surface is generated by a conic section--a curve formed by
the intersection of a plane and a cone--rotating about its principal
axis. Kepler's additional solids are generated by rotation about
lines in the plane of the conic section other than its principal
axis.

While he was in Linz, Kepler published his Epitome Astronomiae
Copernicanae (1618-21; Epitome of Copernican Astronomy). He modelled
this title after the highly successful introduction to astronomy that
had been published by his former Tbingen professor in a number of
editions. But, whereas Mstlin had deemed it prudent pedagogical
practice to keep Copernicanism out of an elementary textbook, which
he therefore entitled simply "Epitome of Astronomy," Kepler
emphasized his open espousal of the new cosmology by inserting the
provocative label "Copernican."

In Linz in 1620, Kepler heard that his mother had been indicted on
the charge of being a witch. Such a defendant was often subjected to
torture and, if convicted, was usually burned at the stake. If his
mother had suffered this fate, Kepler's own status as imperial
mathematician of the Holy Roman Empire and mathematician of Upper
Austria might have been irreparably impaired. He rushed to her
defense, therefore, not only out of filial devotion but also out of
prudent self-interest. Only his skillful intervention saved her from
torture and a fiery death.

Kepler had planned to publish his Tabulae Rudolphinae (Rudolphine
Tables), named in honour of his first imperial patron, Rudolph II, in
Linz. But this work, the final outcome of long years of unceasing
reflection and tireless calculation, could not be printed there
because of a rebellion by the peasants, who were infuriated by a
combination of being forced to return to Catholicism and to pay heavy
taxes. Kepler had to find another home and a new patron.

Albrecht von Wallenstein, duke of Friedland and Zagan, a successful
soldier of fortune who had put his private army at the disposal of
the empire in the Thirty Years' War, accepted the responsibility of
satisfying Kepler's financial needs. The astronomer moved to Zagan
in Silesia, where he was able to establish his own printing press.
The Rudolphine Tables were printed at Ulm, Germany, in 1627, before
Kepler went to Zagan in 1628. But Wallenstein turned out to be
someone on whom Kepler could not rely.

Leaving his family behind in Zagan, Kepler went west to collect the
interest due on two promissory notes he held in exchange for money he
had deposited in Austria. On his way he stopped at Regensburg, where
the Imperial Diet was in session. He fell acutely ill and died on
November 15, 1630. The tremendous upheavals suffered by Germany in
the Thirty Years' War later obliterated his grave.